What can be done If an heir doesn't pay their portion of the bills? Can they forfeit their share?

You do not have to have the consent of all of the heirs in order to have an administrator appointed for an intestate estate, although if you do you can make things easier and less costly by requesting a waiver of bond and the grant of certain powers as part of the Petition for Letters of Administration.  In general, heirs to an estate are not responsible for estate debts or estate administration expenses. However, if this is a Georgia house, then under Georgia law the heirs to an intestate (no Will) estate such as your mother's can become personally responsible for at least certain expenses which come up after the owner's death and which are directly related to ownership of the house. The court case which created that rule involved condominium association fees; it's not currently clear how far that would extend. It might help if you explain to Sister X that she's only costing herself money by delaying and not returning the Petition for Letters of Administration, and that she can be held personally responsible for a share of expenses related to the house if she does not sign the Petition and get it back to you. Once the Administrator has been appointed, the heirs are no longer responsible for paying expenses, however. At that point, the estate's other assets should be used to pay the expenses. If there aren't enough other estate assets, then the house should be sold as soon as possible, and any equity should be used to pay any unpaid estate debts and expenses at that point. Other heirs cannot prevent your sister from receiving her share of any remaining estate assets after the estate administration is completed just because they contributed assets to the estate. The heirs who do contribute assets can be repaid from the estate's assets before the assets are divided up, however. If the proposed Administrator is not already working with an estate attorney, please get one involved as soon as possible. A recalcitrant heir is bad news and makes the process much more difficult, and the Administrator should be very careful anyhow in order to avoid himself (or herself) becoming personally liable for estate-related debts or expenses by paying debts and expenses in the wrong order of priority, or distributing assets to heirs before all debts and expenses are paid in full first.